I have mice in my apartment.Im scared....?

I have been hearing mouse noises lately and a few days ago I saw the first mouse in my apartment in my kitchen. My husband was able to get 2 mice out of the house by barracading and pushing them out the door with the broom. We have since seen another one in the kitchen that likes to stay under kitchen sink,oven and refrigerator. we have not been able to get that one. I contacted my leasing office and they said they would have the exterminator that usually comes out to spray for bugs every month, come spray for mice. Ok, so i asked her if spraying would get rid of the mice and she said most definitely! But I have never heard of removing mice by spraying for them. Will this kill them or get rid of them? And if it does kill them wont they die someowhere and leave a stink in my place? I keep my place pretty clean and just disgusted with this mice problem..im scared!